The fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) based on Skyrme-type interaction is used to study the existence problem of proton semi-bubble structure in the 2 Si is mainly caused by proton transiton from π1d 5/2 orbit to π2s 1/2 orbit, and the existence of a proton semi-bubble structure in this state is very unlikely.
We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom's Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme, where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.
The Hartree-Fock-Bogolyubov (HFB) plus proton-neutron quasiparticle random phase approximation (pnQRPA) approach based on Skyrme interaction is applied to study the nuclear β + /EC decay for nuclei near the proton magic numbers Z =20, 28, and 50. With properly selected Skyrme interactions that include the tensor terms, and the T = 0 pairing interaction, the experimental β + /EC decay half-lives of these nuclei can be systematically reproduced quite well. It is shown that the tensor and T = 0 pairing interactions play different roles in different nuclei. The specific effect is relevant to the configurations that contribute to the decay. The attractive and repulsive properties of tensor interaction for the GT state is also studied. The present results indicate that it works repulsively on the GT states dominated by the configurations from πj ≷ to νj ≷ orbits, while working attractively for those mainly composed of the configurations from πj ≷ to νj ≶ orbits.
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